Site name

You can put CSS to hide the site title.
.site-title {display: none}
That will affect every page. If you want to affect only the home page, use
.home .site-title {display: none}

But it hides the link to Home.

I’m wondering if you mean this:

Is there a way to hide the site title heading above the navigation menu, without changing your site name in Settings?

If that’s what you mean, you could add the following in Appearance > Customize > CSS

.title-area {
  border: 0;
  clip: rect(0, 0, 0, 0);
  height: 1px;
  margin: -1px;
  overflow: hidden;
  padding: 0;
  position: absolute;
  white-space: nowrap;
  width: 1px;
}

This will keep the site title accessible for screen readers, but remove it from layout.

https://snook.ca/archives/html_and_css/hiding-content-for-accessibility